Detection of dead code.

FEM/LagP_node_ref.v

@@ -88,6 +88,7 @@ intros idk jdk; rewrite !node_ref_eqF;
     move=> /(scal_reg_r_R _ (INR_inv_n0 Hk)) /(mapF_inj INR_eq) /Adk_inj; easy.
 Qed.
 
+(* Unused!
 Lemma vtx_node_ref : (0 < k)%coq_nat -> invalF vtx_ref node_ref.
 Proof.
 intros Hk i; destruct (ord_eq_dec i ord0) as [-> | Hi].
@@ -96,7 +97,7 @@ exists (Adk_inv d k (itemF d k (lower_S Hi)));
     rewrite vtx_ref_S node_ref_eqF Adk_kron.
 extF j; rewrite fct_scal_eq scal_eq_K mult_assoc
     (mult_inv_l (INR_invertible Hk)) mult_one_l; easy.
-Qed.
+Qed.*)
 
 (**
  #<A HREF="##RR9557v1">#[[RR9557v1]]#</A>#
@@ -118,13 +119,14 @@ Lemma node_ref_Hface_ref_S :
     Hface_ref i (node_ref idk) <-> Adk d k idk (lower_S Hi) = O.
 Proof. intros; rewrite Hface_ref_S_eq; apply node_ref_ASdki; easy. Qed.
 
+(* Unused!
 Lemma node_ref_Hface_ref_S_old :
   forall (idk : 'I_((pbinom d k).+1)) (i : 'I_d),
     (0 < d)%coq_nat -> (0 < k)%coq_nat ->
     Hface_ref (lift_S i) (node_ref idk) <-> Adk d k idk i = O.
 Proof.
 intros; rewrite (node_ref_Hface_ref_S _ (lift_S_not_first _))// lower_lift_S//.
-Qed.
+Qed.*)
 
 End Node_ref_Facts1.
 
@@ -187,14 +189,14 @@ Qed.
 Lemma node_vtx_ref_d1 : node_ref = castF (eq_sym (pbinomS_1_r d)) vtx_ref.
 Proof. intros; rewrite eq_sym_equiv -castF_sym_equiv -vtx_node_ref_d1//. Qed.
 
-(* Useless? *)
+(* Useless!
 Lemma LagPd1_ref_decomp_node :
   forall {p}, Pdk d 1 p ->
     p = lin_comb (mapF p node_ref) (castF (eq_sym (pbinomS_1_r d)) LagPd1_ref).
 Proof.
 intro; rewrite node_vtx_ref_d1 mapF_castF lc_castF;
     apply LagPd1_ref_decomp_vtx.
-Qed.
+Qed.*)
 
 End Node_ref_d1.
 
@@ -214,6 +216,7 @@ Variable vtx : 'R^{d.+1,d}.
 Definition sub_vtx_ref : 'I_d.+1 -> 'R^d :=
   mapF (scal (INR k.-1 / INR k)) vtx_ref.
 
+(* Unused!
 (**
  #<A HREF="##RR9557v1">#[[RR9557v1]]#</A>#
  Def 1594 (for [vtx_ref] and i=0), Eq (9.88), p. 98.#<BR>#
@@ -222,8 +225,9 @@ Lemma sub_vtx_ref_0 : forall {i}, i = ord0 -> sub_vtx_ref i = vtx_ref ord0.
 Proof.
 intros; subst; unfold sub_vtx_ref;
     rewrite mapF_correct vtx_ref_0// scal_zero_r; easy.
-Qed.
+Qed.*)
 
+(* Unused!
 (**
  #<A HREF="##RR9557v1">#[[RR9557v1]]#</A>#
  Def 1594 (for [vtx_ref] and i<>0), Eq (9.88), p. 98.#<BR>#
@@ -237,22 +241,24 @@ intros Hk i Hi; unfold sub_vtx_ref; rewrite node_ref_eqF Adk_inv_correct_r//;
 rewrite mapF_itemF_0; [| apply INR_0]; extF j.
 rewrite itemF_kron_eq !fct_scal_eq -scal_eq_K scal_assoc mult_comm_R.
 rewrite mapF_correct vtx_ref_S div_eq; easy.
-Qed.
+Qed.*)
 
+(* Unused!
 Lemma LagPd1_ref_sub_vtx_0 :
   forall i, i = ord0 -> LagPd1_ref^~ (sub_vtx_ref i) = itemF d.+1 1 i.
 Proof.
 intros; subst; rewrite sub_vtx_ref_0// LagPd1_ref_kron_vtx_r itemF_kron_eq.
 extF j; rewrite mult_one_l; easy.
-Qed.
+Qed.*)
 
+(* Unused!
 Lemma LagPd1_ref_sub_vtx :
   (0 < k)%coq_nat -> forall i, i <> ord0 ->
     LagPd1_ref^~ (sub_vtx_ref i) = itemF d.+1 (INR k.-1 / INR k) i.
 Proof.
 intros; rewrite sub_vtx_ref_S//.
 
-Admitted.
+Admitted.*)
 
 End Sub_vertices_ref_Def.